Nuclear magnetic resonance gas isotherm technique to evaluate reservoir rock wettability

ABSTRACT

Nuclear magnetic resonance (NMR) gas isotherm techniques to evaluate wettability of porous media, such as hydrocarbon reservoir rock, can include constructing a NMR gas isotherm curve for a porous media sample gas adsorption under various pressures. A hydrophobic or hydrophilic nature of the porous media sample can be determined using the NMR gas isotherm curves. A wettability of the porous media sample can be determined based on the NMR gas isotherm curve. The wettability can be determined for porous media samples with different pore sizes. In the case of reservoir rock samples, the determined wettability can be used, among other things, to model the hydrocarbon reservoir that includes such rock samples, to simulate fluid flow through such reservoirs, or to model enhanced hydrocarbon recovery from such reservoirs.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of and claims the benefitof priority under 35 USC § 120 to U.S. patent application Ser. No.15/463,679, filed Mar. 20, 2017, which is a continuation of U.S. patentapplication Ser. No. 15/069,650, filed Mar. 14, 2016, now Issued as U.S.Pat. No. 9,599,581, issued on Mar. 21, 2017; which claims the benefit ofpriority under 35 USC § 119(e) to U.S. Provisional Application Ser. No.62/151,079, filed on Apr. 22, 2015 and U.S. Provisional Application Ser.No. 62/276,120, filed on Jan. 7, 2016, the contents of each and all ofwhich are hereby incorporated by reference in its respective entirety.

TECHNICAL FIELD

This specification relates to exploration and production ofhydrocarbons, and, more specifically, to detecting reservoir properties.

BACKGROUND

Rocks in a hydrocarbon reservoir store hydrocarbons (for example,petroleum, oil, gas, or combinations of one or more of them), forexample, by trapping the hydrocarbons within porous formations in therocks. Understanding properties of the hydrocarbon reservoir can assistto optimize extraction of the stored hydrocarbons from the reservoir.One technique to understand properties of the hydrocarbon reservoir isto develop computer-generated software models of all or portions of thereservoir. To develop such models, a reservoir rock sample from thehydrocarbon reservoir is evaluated and results of the evaluation areprovided as an input to the computer software program that generates thesoftware models. The reservoir rock sample can be evaluated byperforming one or more of several experiments under laboratoryconditions or under reservoir conditions (that is, the conditionsexperienced by the sample in the hydrocarbon reservoir). Rockwettability, specifically, the wettability of the porous structurewithin the rock, is one of the parameters of the reservoir rock samplethat can be evaluated.

SUMMARY

This specification describes technologies relating to nuclear magneticresonance (NMR) gas isotherm technique to evaluate reservoir rockwettability.

Certain aspects of the subject matter described here can be implementedas a method. Multiple pressures are applied to a three-dimensionalreservoir rock sample in a closed volume. The reservoir rock sampleincludes multiple porous regions distributed along a longitudinal axisof the reservoir rock sample. The multiple porous regions have arespective multiple of wettabilities. Each wettability represents aquality of each porous region to absorb water. At each pressure of themultiple pressure, a spin-echo single-point imaging (SE-SPI) pulsesequence is applied to the multiple porous regions distributed along thelongitudinal axis of the reservoir rock sample. A nuclear magneticresonance (NMR) gas isotherm curve is constructed for the reservoir rocksample in response to applying the multiple pressures. At each pressureof the multiple pressures, the SE-SPI pulse sequence is applied to themultiple porous regions distributed along the longitudinal axis of thereservoir rock sample. The multiple wettabilities are determined for themultiple porous regions based on the NMR gas isotherm curve. Eachwettability of the multiple wettabilities includes a value representingthe quality of each porous region to absorb water. A spatial wettabilitydistribution for the reservoir rock sample is determined based on themultiple wettabilities. The spatial wettability distribution for thereservoir rock sample is provided.

This, and other aspects, can include one or more of the followingfeatures. The NMR gas adsorption isotherm curve can include an NMR watervapor adsorption isotherm curve. It can be determined that the NMR gasisotherm curve is a convex curve. It can be determined that thereservoir rock sample includes more hydrophilic surfaces thanhydrophobic surfaces in response to determining that the NMR gasisotherm curve is a convex curve. It can be determined that the NMR gasisotherm curve is a concave curve. It can be determined that thereservoir rock sample includes more hydrophobic surfaces thanhydrophilic surfaces in response to determining that the NMR gasisotherm curve is a concave curve. The spatial wettability of thereservoir rock sample can be determined based on whether the reservoirrock sample includes more hydrophilic surfaces or more hydrophobicsurfaces. A porosity of the multiple porous regions can range betweenless than a micrometer and greater than a micrometer. To determine thespatial wettability of the rock sample, a first wettability of a firstporous region of the reservoir rock sample having a porosity less than amicrometer can be determined, a second wettability of a second porousregion of the reservoir rock sample having a porosity greater than orequal to a micrometer can be determined. To determine the multiplewettabilities for the multiple porous regions based on the NMR gasisotherm curve, the NMR gas isotherm curve for the reservoir rock samplegas adsorption can be compared with a first standard NMR gas isothermcurve for a hydrophobic sample and a second standard NMR gas isothermcurve for a hydrophilic sample. A NMR gas isotherm curve can beconstructed for the hydrophobic sample. A NMR gas isotherm curve can beconstructed for the hydrophilic sample. The hydrophobic sample includesbeads coated with a hydrophobic coating. The hydrophilic sample includesbeads coated with a hydrophilic coating. To determine the multiplewettabilities for the multiple porous regions based on the NMR gasisotherm curve, a first quantitative value for a first porous regionhaving a porosity ranging less than a micrometer and a secondquantitative value for a second porous region having a porosity ranginggreater than or equal to a micrometer can be determined. To determinethe first quantitative value, a normalized area under the NMR gasisotherm curve can be determined for the first porous region. Todetermine the first value, it can be determined that the reservoir rocksample is water wet in response to determining that the normalized areaunder the curve is between 0 and substantially 0.5, that the reservoirrock sample is intermediate wet in response to determining that thenormalized area under the curve is substantially equal to 0.5, or thatthe reservoir rock sample is water wet in response to determining thatthe normalized area under the curve is between substantially 0.5 and 1.To determine the second value, a ratio of a difference between a watervapor adsorption amount of the reservoir rock sample and a water vaporadsorption amount of the hydrophobic sample and a difference between awater vapor adsorption amount of the hydrophilic sample and the watervapor adsorption amount of the hydrophobic sample can be determined. Todetermine the second quantitative value, it can be determined that thereservoir rock sample is water wet in response to determining that theratio is between 0 and substantially 0.5, that the reservoir rock sampleis intermediate wet in response to determining that the ratio issubstantially equal to 0.5 or that the reservoir rock sample is oil wetin response to determining that the ratio is between substantially 0.5and 1. To determine the second quantitative value, a ratio between awater vapor adsorption of the reservoir rock sample and a water vaporadsorption of the hydrophilic sample can be determined. To apply aSE-SPI pulse sequence at each pressure of the multiple pressures, whileapplying each pressure, the SE-SPI pulse sequence can be applied to themultiple porous regions in the reservoir rock sample, and, for eachporous region, a T2 decay time responsive to the applied pressure can bemeasured.

Certain aspects of the subject matter described here can be implementedas a system. The system includes a nuclear magnetic resonance (NMR)sample call configured to receive a reservoir rock sample includingmultiple porous regions distributed along a longitudinal axis of thereservoir rock sample. The multiple porous regions have respectivemultiple wettabilities. Each wettability represents a quality of eachporous region to absorb water. The system includes a pressure deliverysystem connected to the NMR sample cell. The pressure delivery system isconfigured to apply multiple pressures to the reservoir rock sample inthe NMR sample cell. The system includes a NMR control system connectedto the NMR sample cell. The NMR control system is configured to, at eachpressure of the multiple pressures, apply a spin-echo single-pointimaging (SE-SPI) pulse sequence to the multiple porous regionsdistributed along the longitudinal axis of the reservoir rock sample.The system includes a computer system connected to the NMR controlsystem and the pressure delivery system. The computer system includes acomputer-readable medium storing instructions executable by the computersystem to perform operations. The operations include constructing a NMRgas isotherm curve for the reservoir rock sample in response to applyingthe multiple pressures and, at each pressure, applying the SE-SPI pulsesequence to the multiple porous regions. The operations includedetermining the multiple wettabilities for the multiple porous regionsbased on the NMR gas isotherm curve, each wettability including a valuerepresenting the quality of each porous region to absorb water. Theoperations include determining a spatial wettability distribution forthe reservoir rock sample based on the multiple wettabilities andproviding the spatial wettability distribution for the reservoir rocksample.

This, and other aspects, can include one or more of the followingfeatures. The pressure delivery system can be configured to apply themultiple pressures using water vapor. The NMR gas adsorption isothermcurve includes an NMR water vapor adsorption isotherm curve. Theoperations to determine the multiple wettabilities include determining afirst quantitative value for a first porous region having a porosityranging less than a micrometer. The operations to determine the firstquantitative value include determining that the reservoir rock sample iswater wet in response to determining that the normalized area under thecurve is between 0 and substantially 0.5, that the reservoir rock sampleis intermediate wet in response to determining that the normalized areaunder the curve is substantially equal to 0.5, or that the reservoirrock sample is water wet in response to determining that the normalizedarea under the curve is between substantially 0.5 and 1. The operationsto determine the multiple wettabilities for the multiple porous regionsincludes determining a second quantitative value for a second porousregion having a porosity ranging greater than or equal to a micrometer.The operations include determining that the reservoir rock sample iswater wet in response to determining that the ratio is between 0 andsubstantially 0.5, that the reservoir rock sample is intermediate wet inresponse to determining that the ratio is substantially equal to 0.5, orthat the reservoir rock sample is oil wet in response to determiningthat the ratio is between substantially 0.5 and 1.

Certain aspects of the subject matter described here can be implementedas a method. Multiple pressures are applied to a three-dimensionalreservoir rock sample in a closed volume. The reservoir rock sampleincludes multiple porous regions distributed along a longitudinal axisof the reservoir rock sample. The multiple porous regions haverespective multiple wettabilities. Each wettability represents a qualityof each porous region to absorb water. At each pressure, a NMR pulsesequence is applied to the multiple porous regions distributed along thelongitudinal axis of the reservoir rock sample. A NMR gas isotherm curveis constructed for the rock sample in response to applying the multiplepressures and, at each pressure, applying the NMR pulse sequence. Themultiple wettabilities for the multiple porous regions are determinedbased on the NMR gas isotherm curve. Each wettability includes a valuerepresenting the quality of each porous region to absorb water. Aspatial wettability distribution for the reservoir rock sample isdetermined based on the multiple wettabilities. The spatial wettabilitydistribution is provided for the reservoir rock sample.

This, and other aspects, can include one or more of the followingfeatures. The NMR pulse sequence is either a Carr-Purcell-Meiboom-Gill(CPMG) pulse sequence or a Spin Echo Single Point Imaging (SE-SPI) pulsesequence To construct the NMR gas isotherm for the reservoir rock samplein response to applying the NMR pulse sequence to the multiple porousregions distributed along the longitudinal axis of the reservoir rocksample, while applying each pressure, the NMR pulse sequence can beapplied to the multiple porous regions in the reservoir rock sample,and, for each porous region, a T2 decay time responsive to the appliedpressure can be measured.

The details of one or more implementations of the subject matterdescribed in this specification are set forth in the accompanyingdrawings and the description that follows. Other features, aspects, andadvantages of the subject matter will become apparent from thedescription, the drawings, and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a system for determining a wettabilityof a sample of a reservoir rock sample using the NMR gas isothermtechnique.

FIG. 2 is an example of a workflow for measuring wettability of areservoir rock sample.

FIG. 3 is a schematic diagram of a Carr-Purcell-Meiboom-Gill (CPMG)pulse sequence.

FIGS. 4A-4C are schematic diagrams of a Spin Echo Single Point Imaging(SE-SPI) pulse sequence.

FIG. 5 is a schematic chart of relationships between NMR gas isothermsand surface wettability for reservoir rock samples.

FIG. 6 is a schematic diagram of NMR water vapor isotherm of a porousreservoir rock sample that includes hydrophilic and hydrophobicsurfaces.

FIG. 7 is a schematic plot of sample NMR water vapor isotherm curvesused to quantify wettability of a reservoir rock sample including poresgreater than or equal to a micrometer in size.

FIG. 8 is a schematic plot of sample NMR water vapor isotherm curvesused to quantify wettability of a reservoir rock sample includingsub-micrometer sized pores.

FIG. 9 is a schematic diagram showing example wettability indicesmeasured from a NMR gas isotherm measured using the CPMG pulse sequenceand a NMR gas isotherm measured using the SE-SPI pulse sequence.

FIG. 10 is a flowchart of an example of a process for determining aspatial wettability distribution for a reservoir rock sample.

Like reference numbers and designations in the various drawings indicatelike elements.

DETAILED DESCRIPTION

Rock wettability, specifically, the wettability of the porous structurewithin rocks, is one of the parameters that affect fluid flow throughrocks. Rock wettability, therefore, is an input variable for geophysicalmodels that predict flow through reservoir rocks. Wettability is oftenused as a distinguishing characteristic of reservoir rocks, designatingthe rocks as either hydrophobic or hydrophilic. Wettability is amaterial parameter characteristic of a given rock, for example,sandstone, carbonate or other rock, and additionally depends on factorssuch as surface roughness, surface size, existence of primary adsorptionsites, specific ion effect and other additional factors. One techniqueto determine wettability of a surface (that is, the ability of thesurface to retain moisture) is to add a drop of water to an idealizedsurface and to measure the contact angle of the water on the surface.The determined wettability can be provided as an input variable togeophysical model (a computer-generated or otherwise). The inputvariable will be more accurate and the predictions of the geophysicalmodels will be truer if the wettability were determined for a porousstructure of actual rocks, for example, under conditions that resembleand mimic rock environments.

Macroscopic experiments to determine wettability (for example, contactangle determination experiments) may have limited value to determinewettability within the porous structure of a reservoir rock sample. Somewettability measurement methods (for example, United States Bureau ofMines (USBM) test or Amott-Harvey test) are indirect methods withmultiple experimental procedures which increase the likelihood of errorsin the test results. In addition, both the USBM and Amott-Harvey tests,which measure the wettability of the interior pore surfaces, cannot beperformed under known reservoir conditions.

This specification describes nuclear magnetic resonance (NMR) gasisotherm technique to evaluate rock wettability. The techniquesdescribed in this specification can be implemented to measure global andspatial wettability of a porous structure within a reservoir rocksample. It has been shown that NMR water vapor adsorption isotherm curveshape on the surface of a single-walled carbon nanotube with differentsurface water affinity varies from hydrophobic to hydrophilic. Thisdiscovery shows a direct relationship between wettability andhydrophobicity of a solid surface. Implementing NMR gas isotherm toevaluate the wettability of a reservoir rock sample can provide anaccurate wettability for pores with different sizes includingsub-micrometer sized pores since gas can easily enter such pores.Further, as described later, the NMR gas isotherm technique can becombined with relaxation time (T2) mapping techniques by Spin-EchoSingle Point Imaging (SE-SPI) pulse sequence to provide spatialwettability of the interior pore surface of any porous materialincluding, for example, a sample of a reservoir rock. A comparison ofcertain known wettability measurement techniques with the NMR gasisotherm technique described in this disclosure are shown in the tablebelow.

Wetta- bility of Multiple Under interior Tech- Quanti- MeasurementExper- Reservoir of porous nique tative Time iments Conditions mediaAmmott- Yes, but 10-12 days Yes Yes Yes Harvey ques- tionable USBM Yes,but 1-2 days Yes Yes Yes ques- tionable Contact No 1-2 hrs No Yes NoAngle NMR Yes 1-3 hrs No Yes Yes technique

¹H NMR signal intensity is proportional to the number of ¹H inside adetected sample volume. By monitoring the total amount of surfaceadsorbed ¹H of water vapor peak changes as the confining pressurechanges, NMR water vapor isotherm curve can be constructed. Thewettability measurement based on NMR water vapor isotherm is a directmeasurement which can be conducted under reservoir condition withoutdestroying the sample. The specific characteristics of the isotherm,such as shape and end point, are a function of relative vapor pressurefor hydrophilic and hydrophobic surfaces. For sub-micrometer sizedpores, hydrophilic surfaces produce a convex isotherm while hydrophobicsurfaces produce a concave isotherm. For pores greater than or equal toa micrometer in size, the total amount of adsorbed gas is greater forpores with hydrophilic surfaces compared to those with hydrophobicsurfaces. Thus, the shape or the end point (or both) of an isothermobtained from a reservoir rock sample can enable the determination ofwhether the sample includes hydrophilic or hydrophobic surfaces. Inaddition to the isotherms, ¹H NMR can provide insight into the moleculardynamics at the interface by probing the relaxation processes (T₁, T₂).This additional information can shed light on the interactions betweenthe water molecules and the hydrophilic or hydrophobic surface.

Experimental Systems

FIG. 1 is a schematic diagram of a system 100 for determining awettability of a reservoir rock sample using the NMR gas isothermtechnique. The system 100 includes NMR instrumentation, for example, aNMR control system 102 connected to a NMR magnet, for example, a firstNMR magnet 104 a or a second NMR magnet 104 b or both. The NMRinstrumentation can include either high or low field NMR instruments.The water vapor delivery system 120 includes a vapor expansion bulb,distribution chamber, pressure gauge, pump connection, and NMR samplecell. The NMR sample cell 122 is designed to sustain high pressure andhigh temperature (HPHT) conditions. For example, the NMR sample cell 122can withstand up to 15,000 pounds per square inch (PSI) and up to 250degrees Celsius (° C.) for substantially cylindrical samples of lessthan 5 millimeter (mm) diameter or up to 5, 000 PSI and up to 150° C.for substantially cylindrical samples of about 1.5 inch diameter. Thesample 112 can be any shape of porous media which will have sizeconstraint by the dimension of NMR sample cell 122. The NMR controlsystem 102 is configured to control the NMR instrumentation. Forexample, the NMR control system 102 can provide instructions to the NMRinstrumentation to measure the total amount of protons inside the sampleexcept the structural proton (part of solid). The system 100 can alsoinclude a computer system 108. The computer system 108 can construct theNMR gas isotherms using the total amount of gas (or water vapor)adsorbed on the pore surfaces of porous reservoir rock sample. In someimplementations, the computer system 108 can implement computer softwareoperations to determine a wettability of the sample using techniquesdescribed later.

Each of the control system 102 and the computer system 108 can includeone or more data processing apparatus (for example, one or moreprocessors) and a computer-readable medium storing computer instructionsexecutable by the data processing apparatus to perform operationsincluding constructing NMR gas isotherms for samples and to determinewettabilities of the samples using the NMR gas isotherms. Each of thecontrol system 102 and the computer system 108 can be implemented as adesktop computer, a laptop computer, a personal digital assistant (PDA),a smartphone, a tablet computer, or other computer. Alternatively or inaddition, each of the control system 102 and the computer system 108 canbe implemented as firmware, software, or combinations of them. In someimplementations, the control system 106 and the computer system 108 canbe separate entities, while in some implementations, a single entity(for example, a single computer system) can include both the controlsystem 102 and the computer system 108.

I. Experimental Conditions

A. NMR Gas Adsorption Isotherm Curve Construction

A reservoir rock sample can be placed inside the NMR sample cellincluded in the NMR instrumentation. The sample can include a rock coreplug of any shape. For example, the rock core plug can be a cylindricalsample of substantially 1.5 inch diameter and 2 inch height.Alternatively, the sample can include rock chips (for example, drillcuttings). In other words, any shapes and sizes of porous media samplethat fit into the NMR sample cell can be used.

The NMR experiments described here can be performed under laboratoryconditions (for example, room temperature or pressure or both) or underreservoir conditions (for example, up to 150° C. and pressure up to 5000PSI with the current commercially available technique for sample size of1.5 inch diameter and 2 inches length cylindrical shape). The pressurein the NMR chamber is varied to construct the NMR gas isotherm curves.The initial pressure in the NMR sample cell can be set to any pressure,for example, atmospheric pressure or lower. For example, setting theinitial pressure to the lowest possible pressure can enable a completeconstruction of the NMR gas isotherm curve, which can be beneficial forsub-micrometer sized pore systems. The techniques can be utilized in lowfield (for example, substantially 2 megahertz (MHz) to 20 MHz) or mediumfield (for example, substantially 20 MHz to 43 MHz) or high field (forexample, substantially up to 900 MHz). The relaxation time distribution(T1 and T2) and Fast Fourier Transform (FFT) spectrum can be used toconstruct NMR gas adsorption isotherm curve for low and high field,respectively. The duration of the experiments can depend, in part, onthe experimental setup, field strength, field homogeneity, otherfactors, or combinations of them.

To construct the NMR gas isotherm curve for the sample, the controlsystem 106 can control the NMR instrumentation to measure the NMR gasisotherm starting with a dry sample and sequentially performing NMRmeasurement with while increasing the water vapor pressure within theNMR chamber. That is, the reservoir rock sample can be injected withwater vapor under different pressures to detect adsorbed gas on thesurface. In this manner, the reservoir rock sample can be wetted with anaqueous fluid at different pressures. The NMR instrumentation can detectthe adsorbed water vapor signal and provide the detected information tothe control system 102. Either the control system 106 or the computersystem 108 (or both) can receive time domain raw data from the NMRinstrumentation and invert the time domain raw data to relaxation time(T1 or T2) distribution for low field and FFT spectrum for high fieldNMR used as an input for the wettability calculation described later.

B. Wettability Measurement

FIG. 2 is an example of a workflow 200 for measuring wettability of areservoir rock sample. As described later, wettability of a reservoirrock sample can be quantified by comparing a NMR water vapor isothermconstructed for the reservoir rock sample with NMR water vapor isothermsconstructed for hydrophilic and hydrophobic standards under similarconditions. At 202, pore sizes of the reservoir rock sample can bemeasured by low-field NMR. At 204, standards can be created to match thepore sizes of the reservoir rock sample. For example, beads (forexample, glass beads, polymer beads, or beads made from other material)can be selected to create a pore system having substantially the samepore sizes as the reservoir rock sample. At 206, the standards can beseparated into two batches and each batch can be coated with ahydrophilic coating and a hydrophobic coating, respectively. At 208, NMRgas isotherms can be constructed for the hydrophilic material coatedstandards and the hydrophobic material coated standards. At 210, the NMRgas isotherm of the reservoir rock sample can be compared with the NMRgas isotherms of the hydrophilic material coated standards and thehydrophobic material coated standards to quantify wettability.

II. Wettability Studies

Wetting is the ability of a liquid to maintain contact with a solidsurface, which results from intermolecular interactions when twomaterials are brought together in contact. The wettability, whichmeasures the degree of wetting, is the product of a force balancebetween adhesive and cohesive forces. Adhesion is the tendency of liquidmolecules to create an attraction to a different substance. On the otherhand, cohesion causes the liquid drop to create the minimum possiblesurface area. Hydrophobicity of a solid surface is caused by theadhesive force between liquid and solid. Therefore, wettability of thesolid surface is directly related to hydrophobicity. Wettability studiesare described in this disclosure in the context of reservoir rocksamples, that is, rock samples that can be found in a hydrocarbonreservoir and that can trap hydrocarbons within their pore systems. Thestudies and the findings described in this disclosure can be applicableto any type of porous media, for example, porous media that includehomogeneous pore systems (that is, having pores of substantially samesize) or inhomogeneous pore systems (that is, having multiple poresub-systems, each of different sizes).

The wettability studies can be implemented by applying a magnetic pulsesequence to a porous sample and measuring a NMR gas isotherm and arelaxation time of the pulse sequence. The magnetic pulse sequenceapplied to the sample can include a Carr-Purcell-Meiboom-Gill (CPMG)pulse sequence or a Spin-Echo Single Point Imaging (SE-SPI) pulsesequence. Implementing the CPMG pulse sequence can provide a globalwettability index for a whole sample. Implementing the SE-SPI pulsesequence can provide multiple wettability indices for specific locationswithin the sample.

A. Wettability Studies Using CPMG Pulse Sequence

FIG. 3 is a schematic diagram of a CPMG pulse sequence. The CPMG pulsesequence measures NMR T2 decay time. The T2 decay time measured usingthe CPMG pulse sequences can produce an averaged T2 distribution of theporous sample. A NMR water vapor isotherm can be constructed for theporous sample using techniques described earlier. In someimplementations, a first pressure level is selected and an NMR watervapor isotherm is constructed for the porous sample at the selectedfirst pressure level. The CPMG pulse sequence shown in FIG. 3 is appliedto the porous sample to which the first pressure level is applied andthe T2 decay time is measured. Subsequently, a second pressure level isselected and an NMR water vapor isotherm is constructed for the poroussample at the selected second pressure level. The CPMG pulse sequenceshown in FIG. 3 is applied to the porous sample to which the secondpressure level is applied and the T2 decay time is measured. The stepsof constructing NMR water vapor isotherms and measuring T2 decay time inresponse to the CPMG pulse sequence are repeated for multiple pressurelevels. A pressure-dependent T2 decay profile is created from the T2decay times measured for the different pressure levels. The amount ofgas adsorbed on the pore surface at each pressure can be calculated bymeasuring the total area changes of T2 distribution peak correspondingto the adsorbed gas which is created by inverting time domain T2 decayprofile by CPMG experiment.

B. Wettability Studies Using Two-Dimensional SE-SPI Sequence

FIGS. 4A-4C are schematic diagrams of a SE-SPI pulse sequence. Asdescribed earlier, the NMR gas isotherm technique can be combined withT2 mapping techniques by SE-SPI pulse sequence to provide spatialwettability of the interior pore surface of any porous materialincluding, for example, a sample of a reservoir rock. In suchimplementations, the SE-SPI pulse sequence can replace the CPMG pulsesequence that is used in wettability studies described earlier. TheSE-SPI pulse sequence provides T2 distribution on a specific locationwithin a sample by using a gradient-to-spatial encoding of the NMRsignal. Thus, by combining the T2 mapping technique using the SE-SPIpulse sequence with the NMR gas isotherm method described earlier,spatial wettability distribution within a specific location (or specificlocations) within a pore system can be measured.

In some implementations, a first pressure level is selected and an NMRwater vapor isotherm is constructed for the porous sample at theselected first pressure level. The SE-SPI pulse sequence shown in FIGS.4A-4C are applied to the porous sample to which the first pressure levelis applied and the T2 decay time is measured. Subsequently, a secondpressure level is selected and an NMR water vapor isotherm isconstructed for the porous sample at the selected second pressure level.The SE-SPI pulse sequence shown in FIGS. 4A-4C is applied to the poroussample to which the second pressure level is applied and the T2 decaytime is measured. The steps of constructing NMR water vapor isothermsand measuring T2 decay time in response to the SE-SPI pulse sequence arerepeated for multiple pressure levels. A pressure-dependent T2 decayprofile is created from the T2 decay times measured for the differentpressure levels.

When applying the SE-SPI pulse sequence, the porous sample is dividedinto multiple slices, for example, along a longitudinal axis of thesample. For example, a porous sample that is about 2 inches thick can bedivided into 64 slices. The pressure-dependent T2 decay profile iscreated from the T2 decay times measured for the different pressurelevels in each slice. The amount of gas adsorbed on the each slice ofthe pore surface at each pressure can be calculated by measuring thetotal area changes of T2 distribution peak corresponding to the adsorbedgas which is created by inverting time domain T2 decay profile by SE-SPIexperiment. A wettability index can be determined for each slice usingthe techniques described later. Because each slice is taken at aspecific location in the porous sample, wettability indices can bedetermined for multiple locations in the porous sample.

FIG. 5 is a schematic chart of relationships between NMR gas isothermsand surface wettability for reservoir rock samples. The chart is a plotof adsorption (grams of water divided by grams of grain) versusnormalized pore pressure (P/P₀). The NMR gas isotherm curve is a gasadsorption isotherm curve, specifically, water vapor adsorption isothermcurve. The detected hydrophobicity of the reservoir rock sample surfaceby NMR water vapor isotherm is a direct indication of native wettabilityof rock surface. That is, the surface with more hydrophilic nature willattract more water molecules to be adsorbed and resist hydrocarbonadsorption, and vice versa. FIG. 3 shows three NMR gas isotherm curvesfor three reservoir rock samples with different hydrophobicities.Hydrophobicity of reservoir rock can be divided into threecategories—oil wet (that is, more affinity to hydrocarbons than water,and therefore, hydrophobic), water wet (that is, more affinity to waterthan hydrocarbons, and, therefore, hydrophilic) and intermediate wet(intermediate between oil wet and water wet). The line 302 representsthe NMR gas adsorption isotherm for a water wet reservoir rock sample.The line 304 represents the NMR gas adsorption isotherm for anintermediate wet reservoir rock sample. The line 306 represents the NMRgas adsorption isotherm for an oil wet sample.

FIG. 6 is a schematic diagram 400 of NMR water vapor isotherm of aporous reservoir rock sample that includes hydrophilic and hydrophobicsurfaces. The reservoir rock sample can include multiple pore systems(for example, three pore systems as in FIG. 6), each with a differentpore size. For example, some portions of the rock sample can includesub-micrometer sized pores, some portions of the rock sample can includepores greater than or equal to a micrometer in size, and some portionsof the rock sample can include intermediate-sized pores between thesub-micrometer sized pores and the pores greater than or equal to amicrometer in size. In FIG. 6, the line 402 and the line 404 representhydrophilic surfaces and hydrophobic surfaces, respectively, in such areservoir rock sample with multiple pore systems. In such a rock sample,the NMR water vapor isotherm curve can be a combination of gas isothermcurves depending on the hydrophobicity of each pore system. For example,the hydrophobicity of the pore systems can be hydrophilic for thesub-micrometer sized pores (represented by line 406 in FIG. 6),hydrophobic for the intermediate-sized pores (represented by line 412 inFIG. 6) and hydrophilic for the pores greater than or equal to amicrometer in size (represented by line 414 in FIG. 6). In anotherexample, the hydrophobicity of the pore systems can be hydrophobic forthe sub-micrometer sized pores (represented by line 408 in FIG. 6),hydrophilic for the intermediate-sized pores (represented by line 410 inFIG. 6), and hydrophobic for the pores greater than or equal to amicrometer in size (represented by line 416 in FIG. 6). In otherexamples of mixed-sized pore systems with hydrophilic and hydrophobicsurfaces, the NMR gas adsorption isotherm can include other combinationsof the gas isotherm curves.

The dominant gas adsorption mechanisms for pores greater than or equalto a micrometer in size (diffusion) and sub-micrometer sized pores(capillary condensation) are different. For above-micrometer sized poresystems, water vapor gets adsorbed on the hydrophilic surface (line 414in FIG. 6) in greater amounts and faster as gas pressure is increasedcompared to hydrophobic surfaces (line 416 in FIG. 6). Thus, for poresystems with pores greater than or equal to a micrometer in size, thetotal amount of adsorbed gas can be used for the quantification ofwettability, regardless of the isotherm curve shape.

For sub-micrometer sized pore systems, capillary condensation results inthe same amount of water vapor being adsorbed on the pore surfaceregardless of hydrophobicity. Due to the differences in the adhesionforce between water vapor and the surface for hydrophilic andhydrophobic cases, the shapes of NMR water vapor isotherm curves arealso different. For example, hydrophilic and hydrophobic surfacesproduce concave curve shapes (line 406, line 410 in FIG. 4) and concavecurve shapes (line 408, line 412 in FIG. 4), respectively. Therefore,for sub-micrometer sized pore systems, curve shape analysis can be usedfor the quantification of wettability.

FIG. 7 is a schematic plot 500 of sample NMR water vapor isotherm curvesused to quantify wettability of a reservoir rock sample including poresgreater than or equal to a micrometer in size. In some implementations,the wettability index of such a reservoir rock sample can be calculatedusing Equation 1:

$\begin{matrix}{{WI}_{{{pore}\mspace{14mu}{size}} \geq {micrometer}} = {\frac{S - O}{W - O}.}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

In Equation 1, WI_(pore size≥micrometer) is the wettability index by NMRgas isotherm for above-micrometer sized pore systems. Variables S, O andW represent the total amount of adsorption for sample, 100% oil wetstandard and 100% water wet standard, respectively. For such poresystems, wettability can be quantified by:

Water wet−0.5<WI_(pore size≥micrometer)≤1

Intermediate wet−WI_(pore size≥micrometer)≈0.5

Oil wet−0≤WI_(pore size≥micrometer)<0.5

In some implementations, the NMR water vapor isotherm of standard coatedwith 100% hydrophobic material can be skipped by assuming the variable Oin Equation 1 to be 0, resulting in Equation 2:

$\begin{matrix}{{WI}_{{{pore}\mspace{14mu}{size}} \geq {micrometer}} = {\frac{S}{W}.}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

Surface wetting is caused not only by pore surface chemistry but also byother physical factors, for example, surface roughness, pore structures,or other physical factors. Because Equation 2 does not account for suchphysical factors, a wettability measured using Equation 2, therefore,can be used as an approximation.

FIG. 8 is a schematic plot 600 of sample NMR water vapor isotherm curvesused to quantify wettability of a reservoir rock sample includingsub-micrometer sized pores. The plot 600 shows NMR water vapor isothermcurves for three sub-micrometer sized porous media with differentwettabilties. For a water wet system the NMR water vapor adsorptioncurve is convex and for the oil wet system, the NMR water vaporadsorption curve is concave. In the case of intermediate-wet system theNMR water vapor adsorption curve lies between the convex and concavecurves and is represented as a straight line in FIG. 6. As statedearlier, there is not much difference between the total amounts ofadsorbed water vapor between the surfaces with different wettability forsub-micrometer sized pore systems. Consequently, wettability of areservoir rock sample with sub-micrometer sized pores can be measured bythe differences in curve shape rather than the end points, as wasdescribed earlier for a reservoir rock sample with pore systems withpores greater than or equal to a micrometer in size.

The non-uniform nature of the pore structures can result in thecurvature of the NMR gas isotherm curves not being exactly convex,concave or straight. Therefore, the wettability can be determined bydetermining the area under the curve. To do so, in some implementations,the Trapezoidal rule can be implemented. Alternatively, other techniquesto determine the area under the curve can also be implemented. Thus, insome implementations, the wettability index of a reservoir rock samplewith sub-micrometer sized pores can be calculated using Equation 3 shownbelow.WI_(pore size<micrometer)=Area under NMR gas isotherm curve.  (Equation3)

For such pore systems, wettability can be quantified by:

Water wet−0.5<WI_(pore size<micrometer)≤1

Intermediate wet−WI_(pore size<micrometer)≈0.5

Oil wet−0≤<WI_(pore size<micrometer)<0.5

FIG. 9 is a schematic diagram showing example wettability indicesmeasured from a NMR gas isotherm measured using the CPMG pulse sequenceand a NMR gas isotherm measured using the SE-SPI pulse sequence. Theschematic diagram shows a representation of a porous rock sample 900that includes regions of different wettability. For example, the porousrock sample 900 includes a water-wet region 902, an oil wet region 906and an intermediate wet region 904 having a wettability between those ofthe water-wet region 902 and the oil wet region 906. By implementing NMRgas isotherm measurement using a CPMG pulse sequence, a globalwettability index of 0.4 is determined for the entire porous rocksample. By dividing the sample 900 into three regions and implementingNMR gas isotherm measurement using a SE-SPI pulse sequence in the threeregions, three wettability indices of 0.8, 0.6 and 0.2 are determinedfor the water wet region 902, the intermediate wet region 904 and theoil wet region 906, respectively.

The wettability of the reservoir rock sample, determined by implementingthe techniques described earlier, can be provided as an input variableto the computer system 108 that is executing a geophysical model of thehydrocarbon reservoir that includes reservoir rock substantially similaror identical to the reservoir rock sample. Using the input wettability,the computer system 100 can determine, model or simulate fluid flowthrough the hydrocarbon reservoir. By doing so, the computer system 100can determine a total quantity of hydrocarbon reserve in the hydrocarbonreservoir or determine a production rate or both. In addition, thecomputer system 100 can use the wettability as an input parameter formodels that measure, monitor, model or simulate enhanced oil recovery(EOR) or improved oil recovery (IOR) or both. In this manner,determining the wettability of a reservoir rock sample using the NMR gasadsorption isotherm technique described earlier can improve the accuracyof hydrocarbon reservoir simulation and help design more effectiveEOR/IOR techniques for the target hydrocarbon reservoir.

FIG. 10 is a flowchart of an example of a process 1000 for determining aspatial wettability distribution for a reservoir rock sample. At 1002,multiple pressures are applied to a three-dimensional reservoir rocksample in a closed volume. The reservoir rock sample includes multipleporous regions distributed along a longitudinal axis of the reservoirrock sample. The multiple porous regions have respective multiplewettabilities. Each wettability represents a quality of each porousregion to absorb water. At 1004 and at each pressure, a NMR pulsesequence is applied to the multiple porous regions distributed along thelongitudinal axis of the reservoir rock sample. At 1006, a NMR gasisotherm curve is constructed for the reservoir rock sample in responseto applying the multiple pressures and, at each pressure, applying theNMR pulse sequence to the multiple porous regions distributed along thelongitudinal axis of the reservoir rock sample. At 1008, multiplewettabilities for the multiple porous regions are determined based onthe NMR gas isotherm curve. Each wettability includes a valuerepresenting a quality of each porous region to absorb water. At 1010, aspatial wettability distribution is determined for the reservoir rocksample based on the multiple wettabilities. At 1012, the spatialwettability distribution for the reservoir rock sample is provided. Forexample, the spatial wettability distribution can be displayed on adisplay device as shown in FIG. 9.

Thus, particular implementations of the subject matter have beendescribed. Other implementations are within the scope of the followingclaims. For example, the techniques described above are in the contextof NMR water vapor adsorption isotherms. To study the wettability of thereservoir rock sample using a hydrocarbon fluid, the appropriatehydrocarbon gas can be used instead of water vapor. Doing so can enablemeasuring the wettability for specific gas type in the inner surfaces ofporous media.

The invention claimed is:
 1. A method comprising: with a rock sample ina closed volume, the rock sample comprising a plurality of porousregions distributed along a longitudinal axis of the rock sample,wherein the plurality of porous regions have a respective plurality ofwettabilities, each wettability representing a quality of each porousregion to absorb a gas, for a plurality of pressures applied to the rocksample, applying a spin-echo single-point imaging (SE-SPI) pulsesequence to the plurality of porous regions distributed along thelongitudinal axis of the rock sample at each pressure of the pluralityof pressures; constructing a nuclear magnetic resonance (NMR) gasisotherm curve for the rock sample in response to applying the SE-SPIpulse sequence to the plurality of porous regions distributed along thelongitudinal axis of the rock sample at each pressure of the pluralityof pressures; determining the plurality of wettabilities for theplurality of porous regions based on the NMR gas isotherm curve, eachwettability of the plurality of wettabilities including a valuerepresenting the quality of each porous region to absorb the gas; andproviding the plurality of wettabilities.
 2. The method of claim 1,wherein the NMR gas adsorption isotherm curve comprises an NMR watervapor adsorption isotherm curve.
 3. The method of claim 1, furthercomprising: determining that the NMR gas isotherm curve is a convexcurve; and determining that the rock sample comprises more hydrophilicsurfaces than hydrophobic surfaces.
 4. The method of claim 1, furthercomprising: determining that the NMR gas isotherm curve is a concavecurve; and determining that the rock sample comprises more hydrophobicsurfaces than hydrophilic surfaces.
 5. The method of claim 1, whereinfurther determining a spatial wettability of the rock sample comprisesdetermining the spatial wettability based on whether the rock samplecomprises more hydrophilic surfaces or more hydrophobic surfaces.
 6. Themethod of claim 1, wherein a porosity of the plurality of porous regionsranges between less than a micrometer and greater than a micrometer, andwherein determining a spatial wettability of the rock sample comprises:determining a first wettability of a first porous region of the rocksample having a porosity less than a micrometer; and determining asecond wettability of a second porous region of the rock sample having aporosity greater than or equal to a micrometer.
 7. The method of claim1, wherein determining the plurality of wettabilities for the pluralityof porous regions based on the NMR gas isotherm curve, each wettabilityof the plurality of wettabilities including a value representing thequality of each porous region to absorb water comprises: comparing theNMR gas isotherm curve for the rock sample gas adsorption with a firststandard NMR gas isotherm curve for a hydrophobic sample and a secondstandard NMR gas isotherm curve for a hydrophilic sample.
 8. The methodof claim 7, further comprising: constructing a nuclear magneticresonance (NMR) gas isotherm curve for the hydrophobic sample; andconstructing a nuclear magnetic resonance (NMR) gas isotherm curve forthe hydrophilic sample.
 9. The method of claim 8, wherein thehydrophobic sample comprises beads coated with a hydrophobic coating,and wherein the hydrophilic sample comprises beads coated with ahydrophilic coating.
 10. The method of claim 1, wherein determining theplurality of wettabilities for the plurality of porous regions based onthe NMR gas isotherm curve, each wettability of the plurality ofwettabilities including a value representing the quality of each porousregion to absorb water comprises: determining a first quantitative valuefor a first porous region having a porosity ranging less than amicrometer; and determining a second quantitative value for a secondporous region having a porosity ranging greater than or equal to amicrometer.
 11. The method of claim 10, wherein determining the firstquantitative value comprises determining a normalized area under the NMRgas isotherm curve for the first porous region.
 12. The method of claim11, wherein determining the first quantitative value comprisesdetermining that the rock sample is oil wet in response to determiningthat the normalized area under the curve is between 0 and substantially0.5, determining that the rock sample is intermediate wet in response todetermining that the normalized area under the curve is substantiallyequal to 0.5, or determining that the rock sample is water wet inresponse to determining that the normalized area under the curve isbetween substantially 0.5 and
 1. 13. The method of claim 11, whereindetermining the second quantitative value comprises determining a ratioof a difference between a water vapor adsorption amount of the rocksample and a water vapor adsorption amount of the hydrophobic sample anda difference between a water vapor adsorption amount of the hydrophilicsample and the water vapor adsorption amount of the hydrophobic sample.14. The method of claim 13, wherein determining the second quantitativevalue comprises determining that the rock sample is oil wet in responseto determining that the ratio is between 0 and substantially 0.5,determining that the rock sample is intermediate wet in response todetermining that the ratio is substantially equal to 0.5, or determiningthat the rock sample is water wet in response to determining that theratio is between substantially 0.5 and
 1. 15. The method of claim 11,wherein determining the second quantitative value comprises determininga ratio between a water vapor adsorption of the rock sample and a watervapor adsorption of the hydrophilic sample.
 16. The method of claim 1,wherein, at each pressure of the plurality of pressures, applying aSE-SPI pulse sequence to the plurality of porous regions distributedalong the longitudinal axis of the rock sample comprises, while applyingeach pressure: applying the SE-SPI pulse sequence to the plurality ofporous regions in the rock sample; and for each porous region, measuringa T2 decay time responsive to the applied pressure.